Volume Of Triakis Tetrahedron Given Surface To Volume Ratio Calculator

Volume Of Triakis Tetrahedron Given Surface To Volume Ratio Formula:

\[ V = \frac{3}{20} \times \sqrt{2} \times \left( \frac{4 \times \sqrt{11}}{RA/V \times \sqrt{2}} \right)^3 \]

Volume of Triakis Tetrahedron:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Volume of Triakis Tetrahedron?

The Volume of Triakis Tetrahedron is the quantity of three dimensional space enclosed by the entire surface of Triakis Tetrahedron. It represents the total capacity or space occupied by this geometric shape.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V = \frac{3}{20} \times \sqrt{2} \times \left( \frac{4 \times \sqrt{11}}{RA/V \times \sqrt{2}} \right)^3 \]

Where:

\( V \) — Volume of Triakis Tetrahedron (m³)
\( RA/V \) — Surface to Volume Ratio of Triakis Tetrahedron (1/m)
\( \sqrt{2} \) — Square root of 2 (approximately 1.4142)
\( \sqrt{11} \) — Square root of 11 (approximately 3.3166)

Explanation: This formula calculates the volume of a triakis tetrahedron based on its surface to volume ratio, using mathematical constants and geometric relationships specific to this polyhedron.

3. Importance of Volume Calculation

Details: Calculating the volume of geometric shapes is fundamental in mathematics, engineering, architecture, and various scientific fields. It helps in determining capacity, material requirements, and spatial relationships in three-dimensional objects.

4. Using the Calculator

Tips: Enter the surface to volume ratio of the triakis tetrahedron in 1/m. The value must be greater than zero. The calculator will compute the corresponding volume based on the geometric formula.

5. Frequently Asked Questions (FAQ)

Q1: What is a Triakis Tetrahedron?
A: A triakis tetrahedron is a Catalan solid that can be constructed by attaching triangular pyramids to each face of a regular tetrahedron.

Q2: What are the units for surface to volume ratio?
A: Surface to volume ratio is typically measured in 1/m (inverse meters), representing the surface area per unit volume.

Q3: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to triakis tetrahedra. Different polyhedra have different volume formulas based on their unique geometric properties.

Q4: What is the significance of the constants in the formula?
A: The constants √2 and √11 arise from the geometric properties and trigonometric relationships inherent in the structure of the triakis tetrahedron.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the geometric properties of a perfect triakis tetrahedron. Real-world applications may require adjustments for manufacturing tolerances or material properties.